TS EAMCET · Maths · Circle
If \(A=(0,-2)\) and \(B\) is any point on the circle \(x^2+y^2-2 x-2 y+1=0\), then the maximum value of \((\overline{A B})^2\) is
- A 51
- B \(11+2 \sqrt{10}\)
- C \(9+3 \sqrt{5}\)
- D \(\frac{5+2 \sqrt{3}}{2}\)
Answer & Solution
Correct Answer
(B) \(11+2 \sqrt{10}\)
Step-by-step Solution
Detailed explanation
Given point \(\mathrm{A}=(0,-2)\) and \(\mathrm{B}\) is a point on the circle \(x^2+y^2-2 x-2 y+1=0\) \((\overline{\mathrm{AB}})_{\max }=\mathrm{r}+\mathrm{cB}\) (where \(\mathrm{C}\) is centre of the circle) \(=1+\sqrt{10}\) Now \((\overline{\mathrm{AB}})^2=11+2 \sqrt{10}\)
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